Heuristic Examples Research Articles

Working with an instructional video on mathematical modeling: upper-secondary students’ perceived advantages and challenges

Many instructional videos in mathematics education target knowledge of procedures and algorithms. To design instructional videos that support students in a non-algorithmic domain, such as mathematical modeling, we developed a framework based on research on heuristic worked examples and instructional videos. Because students’ perceptions play an important role in whether they will engage with a learning resource, our research questions focus on the advantages and challenges students perceive when they work with an instructional video on mathematical modeling and solve a subsequent related modeling problem. Using a video based on the developed framework, we conducted an interview study with 14 pairs of upper-secondary students. The results of the qualitative text analysis showed that the perceived advantages and challenges were related to certain design features and to the processes of self-regulated learning with the video. The students experienced challenges regarding the video’s duration, the transfer to a subsequent related modeling problem, the absence of a teacher, and self-discipline. Hence, further learner support is necessary to guide the transition from working with a video to autonomous modeling, such as combining the video with strategic instruments and teacher support. In addition, interactive video features may be essential, as the students enjoyed how those features involved them in the process of watching the video. Overall, the results indicate that instructional videos are promising for providing heuristic worked examples, offering an innovative approach for teaching and learning mathematical modeling.

Az antropocén és a performatív tudomány : Példák a Bielefeldi Egyetemről

This study inquires how theatrality and performativity (drama pedagogy) played an important role in certain research and teaching programs of the Center of Interdisciplinary Research in Bielefeld (Zentrum für interdisziplinäre Forschung / ZIF) and its associated Bielefeld University. It focuses especially on heuristic examples engaging with the challenges of the Anthropocene. By using inside and outside perspectives to the topic, the study investigates the structure of a university seminar on performing science, as well as the intersection, where art and science meet productively in a universitarian framework.

HexFire: A Flexible and Accessible Wildfire Simulator.

As fire frequency and severity grow throughout the world, scientists working across a range of disciplines will increasingly need to incorporate wildfire models into their research. However, fire simulators tend to be highly complex, time-consuming to learn, and difficult to parameterize. As a result, embracing these models can prove impractical for scientists and practitioners who are not fire specialists. Here we introduce a parsimonious wildfire simulator named HexFire that has been designed for rapid uptake by investigators who do not specialize in the mechanics of fire spread. HexFire should be useful to such nonspecialists for representing the spread of fire, interactions with fuel breaks, and for integrating wildfire into other types of ecological models. We provide a detailed description of the HexFire simulator's design and mechanisms. Our heuristic fire spread examples highlight the flexibility inherent in the model system, demonstrate that HexFire can generate a wide range of emergent fire behaviors, and illustrate how HexFire might be coupled with other environmental models. We also describe ways that HexFire itself might be altered or augmented. HexFire can be used as a proxy for more detailed fire simulators and to assess the implications of wildfire for local ecological systems. HexFire can also simulate fire interactions with fuel breaks and active fire suppression.

Using heuristic worked examples to promote solving of reality-based tasks in mathematics in lower secondary school

This study examined whether learning with heuristic worked examples can improve students’ competency in solving reality-based tasks in mathematics (mathematical modeling competency). We randomly assigned 134 students in Grade 5 and 180 students in Grade 7 to one of three conditions: control condition (students worked on reality-based tasks), worked example condition (students studied worked examples representing a realistic process of problem-solving by fictitious students negotiating solutions to the tasks), and prompted worked example condition (students additionally received self-explanation prompts). In all three conditions, the students worked on the tasks individually and independently for 45 min. Dependent measures were mathematical modeling competency (number of adequate solution steps and strategies) and modeling-specific strategy knowledge. Results showed that although strategy knowledge could be improved through the intervention for fifth and seventh graders, modeling competency was improved only for seventh graders. The prompting of self-explanations had no additional effect for either fifth or seventh graders.

Adaptable scaffolding of mathematical argumentation skills: The role of self-regulation when scaffolded with CSCL scripts and heuristic worked examples

Collaboration scripts and heuristic worked examples have been described as powerful scaffolds to support skill acquisition in CSCL. While CSCL scripts particularly facilitate argumentative discourse within groups, heuristic worked examples provide heuristics and worked out pathways to solve domain-specific tasks. Yet, both scripts and heuristic worked examples are often designed in a one-size-fits-all fashion. Granting learners the opportunity to adapt these scaffolds to their self-perceived needs might be a way to further enhance their effects. We tested this assumption in two experiments. In experiment 1, we compared the effects of learning with adaptable and non-adaptable CSCL scripts. In experiment 2, we compared the effects of learning with adaptable and non-adaptable heuristic worked examples. University students (N = 167) learned repeatedly in pairs with either adaptable or non-adaptable scaffolding in the context of mathematical conjecture problems. Results show that adaptable CSCL scripts were partly helpful for students with higher levels of self-regulation skills. Non-adaptable maximal scaffolding supported learning of distinctive skill components. Social-discursive components were best facilitated by maximal heuristic worked examples through content knowledge scaffolds. In contrast, CSCL scripts best facilitated domain-specific skill components by scaffolding learners’ engagement in social discourse about domain knowledge. The study provides recommendations for designing adaptable scaffolding by taking into account the relation between the targeted skill component and the activities scaffolded in the learning process. We suggest conducting future studies on adaptable scaffolding with a focus on supporting learning regulation and group awareness to improve learners’ success in CSCL environments.

Antibunching and superbunching photon correlations in pseudo-natural light

Since Hanbury Brown and Twiss revealed the photon bunching effect of a thermal light source in 1956, almost all studies in correlation optics have been based on light’s intensity fluctuation, regardless of fact that the polarization fluctuation is a basic attribute of natural light. In this work, we uncover the veil of the polarization fluctuation and corresponding photon correlations by proposing a new light source model, termed pseudo-natural light, embodying both intensity and polarization fluctuations. Unexpectedly, the strong antibunching and superbunching effects can be simultaneously realized in such a new source, whose second-order correlation coefficient g ( 2 ) can be continuously modulated across 1. For the symmetric Bernoulli distribution of the polarization fluctuation, particularly, g ( 2 ) can be in principle from 0 to unlimitedly large. In pseudo-natural light, while the bunching effects of both intensity and polarization fluctuations enhance the bunching to superbunching photon correlation, the antibunching correlation of the polarization fluctuation can also be extracted through the procedure of division operation in the experiment. The antibunching effect and the combination with the bunching one will arouse new applications in quantum imaging. As heuristic examples, we carry out high-quality positive or negative ghost imaging, and devise high-efficiency polarization-sensitive and edge-enhanced imaging. This work, therefore, sheds light on the development of multiple and broad correlation functions for natural light.

Exposure of cultural resources to 21st-century climate change: Towards a risk management plan

Anthropogenic climate change during the 21st century presents a significant challenge to the protection of cultural resources (CRs) on federal lands that encompass ∼ 28% of the U.S. In particular, CRs on this land base may be adversely affected by a wide range of climate-change hazards, including damage by sea-level rise, enhanced deterioration by increasing temperature and precipitation, and destruction by more-frequent and severe wildfire. Most current measures to manage the impacts of hazards on CRs use vulnerability assessments, but because these require that all CRs be treated as having an equal chance of being affected by climate-change hazards (i.e., equal exposure) across large landscapes, the cost and resources required for such analyses are overwhelming to land management agencies. Projections of changes in many hazards, however, show that the probability of hazard occurrence will be unevenly distributed on the landscape. Incorporating this information into a risk assessment thus allows CR managers to prioritize their efforts on assessing impacts to CRs in those areas where the probability of the hazard is greatest, thus increasing efficiency. We provide several heuristic examples of implementing the first part of a CR risk assessment by using 21st-century projections of several hazards most likely to adversely affect CRs on nine National Forests (NFs) managed by the U.S. Forest Service in northern Idaho and Montana. Overlaying the projected distribution of hazards on these NFs with the distribution of CRs identifies CR exposure that, with information on their vulnerability, is required to determine risk. Additional policy and field studies will be needed to determine how to prioritize those CRs that are most at risk according to their significance as well as identify how impacts can be reduced and managed through adaptation planning and implementation. Adaptation will follow the iterative risk management process particularly by improving projection resolution. Finer scale, process-based modeling informed by the highest priority CRs would also provide a means to assess various adaptation options that might change the estimated risk and increase the odds of CRs being as little affected as possible.

Four major literary code-switching strategies in Hungarian literature. Decoding monolingualism

Abstract The field of literary multilingualism has quickly grown over the last decades. Multiple studies have examined the way linguistic diversity manifests itself in literature by focusing on specific strategies such as code-switching, code-mixing, code-shifting, hybridization, etc. However, the current understanding of multilingual practices is still dominated by a remarkable terminological inconsistency. In this article, we provide a new theoretical framework called ‘literary code-switching’ (Domokos 2018–2020), that can be used to examine most literary multilingual practices – from the most hidden or latent to the more manifest ones. This formulation, which is scaled into degrees from 0 to 5, will be applied to some key examples taken from the works of Imre Madách, Mihály Tompa, Imre Oravecz, Attila Jász, Ferenc Karinthy, Terézia Mora and Anne Tardos. The aim of picking up these heuristic examples from Hungarian literature is to point towards the necessity of investigating literature more systematically according to its hidden and manifest linguistic diversity.

Contemporary Issues in Reporting Statistical, Practical, and Clinical Significance in Counseling Research

Null hypothesis statistical testing (NHST) represents a primary method of addressing quantitative results in counseling research. The use of NHST and the expression of results are often limited to the populations of interest, and many studies may not be replicable. Furthermore, the communication of results in terms of practical and clinical significance is not simply an extension of NHST but rather a necessary endeavor to communicate accurate and useful results. Communication and elucidation of effect size and confidence intervals, presentation of visual depictions of data, and alternative measures to express clinical significance are highlighted. Limitations of NHST, the necessary results to illuminate findings related to NHST, and heuristic examples for counseling researchers when reporting the results of their studies are provided. Further emphasis on the aforementioned areas will enhance understanding of results to stakeholders and increase the functionality and scholarly utility of counseling research.

Art Making Through Change: New Journeys with Gender and Identity

Creative Arts Educ Ther (2018) 4(2):214–224 DOI: 10.15212/CAET/2018/4/32 Art Making Through Change: New Journeys with Gender and Identity Abstract This paper discusses the role of the art making process within art therapy to support experiences of change, loss, and new identities, where themes of social change, pioneering and new narratives create challenge and opportunity for those within the therapeutic art making space. The paper discusses a heuristic art-based process, and examples and considerations for art therapy group work practice in relation to gender transition, and non-binary identity.

Evaluating Evidence Regarding Relationships With Criteria

ABSTRACTAn overview of standards related to demonstrating evidence regarding relationships with criteria as it pertains to instrument development was presented, along with heuristic examples. Additional measures and a comprehensive design are necessary to establish evidence related to the use and interpretation of test scores for the validation of a measure.

How to combine collaboration scripts and heuristic worked examples to foster mathematical argumentation – when working memory matters

Mathematical argumentation skills (MAS) are considered an important outcome of mathematics learning, particularly in secondary and tertiary education. As MAS are complex, an effective way of supporting their acquisition may require combining different scaffolds. However, how to combine different scaffolds is a delicate issue, as providing learners with more than one scaffold may be overwhelming, especially when these scaffolds are presented at the same time in the learning process and when learners’ individual learning prerequisites are suboptimal. The present study therefore investigated the effects of the presentation sequence of introducing two scaffolds (collaboration script first vs. heuristic worked examples first) and the fading of the primarily presented scaffold (fading vs. no fading) on the acquisition of dialogic and dialectic MAS of participants of a preparatory mathematics course at university. In addition, we explored how prior knowledge and working memory capacity moderated the effects. Overall, 108 university freshmen worked in dyads on mathematical proof tasks in four treatment sessions. Results showed no effects of the presentation sequence of the collaboration script and heuristic worked examples on dialogic and dialectic MAS. Yet, fading of the initially introduced scaffold had a positive main effect on dialogic MAS. Concerning dialectic MAS, fading the collaboration script when it was presented first was most effective for learners with low working memory capacity. The collaboration script might be appropriate to initially support dialectic MAS, but might be overwhelming for learners with lower working memory capacity when combined with heuristic worked examples later on.

Matching synchrosqueezing transform: A useful tool for characterizing signals with fast varying instantaneous frequency and application to machine fault diagnosis

Abstract Synchrosqueezing transform (SST) can effectively improve the readability of the time-frequency (TF) representation (TFR) of nonstationary signals composed of multiple components with slow varying instantaneous frequency (IF). However, for signals composed of multiple components with fast varying IF, SST still suffers from TF blurs. In this paper, we introduce a time-frequency analysis (TFA) method called matching synchrosqueezing transform (MSST) that achieves a highly concentrated TF representation comparable to the standard TF reassignment methods (STFRM), even for signals with fast varying IF, and furthermore, MSST retains the reconstruction benefit of SST. MSST captures the philosophy of STFRM to simultaneously consider time and frequency variables, and incorporates three estimators (i.e., the IF estimator, the group delay estimator, and a chirp-rate estimator) into a comprehensive and accurate IF estimator. In this paper, we first introduce the motivation of MSST with three heuristic examples. Then we introduce a precise mathematical definition of a class of chirp-like intrinsic-mode-type functions that locally can be viewed as a sum of a reasonably small number of approximate chirp signals, and we prove that MSST does indeed succeed in estimating chirp-rate and IF of arbitrary functions in this class and succeed in decomposing these functions. Furthermore, we describe an efficient numerical algorithm for the practical implementation of the MSST, and we provide an adaptive IF extraction method for MSST reconstruction. Finally, we verify the effectiveness of the MSST in practical applications for machine fault diagnosis, including gearbox fault diagnosis for a wind turbine in variable speed conditions and rotor rub-impact fault diagnosis for a dual-rotor turbofan engine.

Nonlinear Analysis in Counseling Research

ABSTRACTNonlinear effects are both underreported and underrepresented in counseling research. We provide a rationale for evaluating nonlinear effects and steps to evaluate nonlinear relationships in counseling research. Two heuristic examples are provided along with discussion of the results and advantages to evaluating nonlinear effects.

Nonlinear Analysis in Counseling Research

Nonlinear effects are both underreported and underrepresented in counseling research. We provide a rationale for evaluating nonlinear effects and steps to evaluate nonlinear relationships in counseling research. Two heuristic examples are provided along with discussion of the results and advantages to evaluating nonlinear effects.

Developing argumentation skills in mathematics through computer-supported collaborative learning: the role of transactivity

Collaboration scripts and heuristic worked examples are effective means to scaffold university freshmen’s mathematical argumentation skills. Yet, which collaborative learning processes are responsible for these effects has remained unclear. Learners presumably will gain the most out of collaboration if the collaborators refer to each other’s contributions in a dialectic way (dialectic transactivity). Learners also may refer to each other’s contributions in a dialogic way (dialogic transactivity). Alternatively, learners may not refer to each other’s contributions at all, but still construct knowledge (constructive activities). This article investigates the extent to which constructive activities, dialogic transactivity, and dialectic transactivity generated by either the learner or the learning partner can explain the positive effects of collaboration scripts and heuristic worked examples on the learners’ disposition to use argumentation skills. We conducted a 2 × 2 experiment with the factors collaboration script and heuristic worked examples with N = 101 math teacher students. Results showed that the learners’ engagement in self-generated dialectic transactivity (i.e., responding to the learning partner’s contribution in an argumentative way by critiquing and/or integrating their learning partner’s contributions) mediated the effects of both scaffolds on their disposition to use argumentation skills, whereas partner-generated dialectic transactivity or any other measured collaborative learning activity did not. To support the disposition to use argumentation skills in mathematics, learning environments should thus be designed in a way to help learners display dialectic transactivity. Future research should investigate how learners might better benefit from the dialectic transactivity generated by their learning partners.

Will Passive Protection Save Congo Forests?

Central Africa’s tropical forests are among the world’s largest carbon reserves. Historically, they have experienced low rates of deforestation. Pressures to clear land are increasing due to development of infrastructure and livelihoods, foreign investment in agriculture, and shifting land use management, particularly in the Democratic Republic of Congo (DRC). The DRC contains the greatest area of intact African forests. These store approximately 22 billion tons of carbon in aboveground live biomass, yet only 10% are protected. Can the status quo of passive protection — forest management that is low or nonexistent — ensure the preservation of this forest and its carbon? We have developed the SimCongo model to simulate changes in land cover and land use based on theorized policy scenarios from 2010 to 2050. Three scenarios were examined: the first (Historical Trends) assumes passive forest protection; the next (Conservation) posits active protection of forests and activation of the national REDD+ action plan, and the last (Agricultural Development) assumes increased agricultural activities in forested land with concomitant increased deforestation. SimCongo is a cellular automata model based on Bayesian statistical methods tailored for the DRC, built with the Dinamica-EGO platform. The model is parameterized and validated with deforestation observations from the past and runs the scenarios from 2010 through 2050 with a yearly time step. We estimate the Historical Trends trajectory will result in average emissions of 139 million t CO2 year-1 by the 2040s, a 15% increase over current emissions. The Conservation scenario would result in 58% less clearing than Historical Trends and would conserve carbon-dense forest and woodland savanna areas. The Agricultural Development scenario leads to emissions of 212 million t CO2 year-1 by the 2040s. These scenarios are heuristic examples of policy’s influence on forest conservation and carbon storage. Our results suggest that 1) passive protection of the DRC’s forest and woodland savanna is insufficient to reduce deforestation; and 2): enactment of a REDD+ plan or similar conservation measure is needed to actively protect Congo forests, their unique ecology, and their important role in the global carbon cycle.

Healthcare cost savings estimator tool for chronic disease self-management program: a new tool for program administrators and decision makers.

Chronic disease self-management education (CDSME) programs have been delivered to more than 100,000 older Americans with chronic conditions. As one of the Stanford suite of evidence-based CDSME programs, the chronic disease self-management program (CDSMP) has been disseminated in diverse populations and settings. The objective of this paper is to introduce a practical, universally applicable tool to assist program administrators and decision makers plan implementation efforts and make the case for continued program delivery. This tool was developed utilizing data from a recent National Study of CDSMP to estimate national savings associated with program participation. Potential annual healthcare savings per CDSMP participant were calculated based on averted emergency room visits and hospitalizations. While national data can be utilized to estimate cost savings, the tool has built-in features allowing users to tailor calculations based on their site-specific data. Building upon the National Study of CDSMP’s documented potential savings of $3.3 billion in healthcare costs by reaching 5% of adults with one or more chronic conditions, two heuristic case examples were also explored based on different population projections. The case examples show how a small county and large metropolitan city were not only able to estimate healthcare savings ($38,803 for the small county; $732,290 for the large metropolitan city) for their existing participant populations but also to project significant healthcare savings if they plan to reach higher proportions of middle-aged and older adults. Having a tool to demonstrate the monetary value of CDSMP can contribute to the ongoing dissemination and sustainability of such community-based interventions. Next steps will be creating a user-friendly, internet-based version of Healthcare Cost Savings Estimator Tool: CDSMP, followed by broadening the tool to consider cost savings for other evidence-based programs.

Teaching GLM Concepts: Explicating the Connections

The purpose of the present paper is to encourage textbook authors, quantitative instructors, curriculum writers, and software developers to move away from the use of isolated apparently disconnected analyses and instead move towards the use of the general linear model as a foundational framework for graduate level statistics training. It is argued that an understanding of modeling, simple linear equations, and commonly used analogous statistical terms will facilitate students understanding of frequently used parametric analyses. Additionally, this holistic approach will equip students with the necessary preparatory skills to understand newer analytical approaches. Three heuristic examples are provided.DOI:10.2458/azu_jmmss_v6i2_skidmore

Teaching GLM Concepts: Explicating the Connections

The purpose of the present paper is to encourage textbook authors, quantitative instructors, curriculum writers, and software developers to move away from the use of isolated apparently disconnected analyses and instead move towards the use of the general linear model as a foundational framework for graduate level statistics training. It is argued that an understanding of modeling, simple linear equations, and commonly used analogous statistical terms will facilitate students understanding of frequently used parametric analyses. Additionally, this holistic approach will equip students with the necessary preparatory skills to understand newer analytical approaches. Three heuristic examples are provided.DOI:10.2458/azu_jmmss_v6i2_skidmore